Diffeomorphisms with positive metric entropy

被引：20
作者：
Avila, A. [1 ,2 ]
Crovisier, S. [3 ]
Wilkinson, A. [4 ]
机构：
[1] UPMC Univ Paris 06, Sorbonne Univ, Sorbonne Paris Cite, CNRS,IMJ PRG,Univ Paris Diderot,UMR 7586, F-75013 Paris, France
[2] IMPA, Estr Dona Castorina 110, Rio De Janeiro, Brazil
[3] Univ Paris Sud 11, CNRS, UMR 8628, Lab Math Orsay, F-91405 Orsay, France
[4] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA
来源：
PUBLICATIONS MATHEMATIQUES DE L IHES | 2016年 / 124卷 / 01期
基金：
美国国家科学基金会;
关键词：
HYPERBOLICITY; GENERICITY;
D O I：
10.1007/s10240-016-0086-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain a dichotomy for -generic, volume-preserving diffeomorphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. nonuniformly hyperbolic and the splitting into stable and unstable spaces is dominated). This completes a program first put forth by Ricardo Ma,.
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收藏
页码：319 / 347
页数：29
相关论文
共 26 条
[1]  
[Anonymous], 1980, I HAUTES ETUDES SCI
[2]  
[Anonymous], 2012, ESSAYS MATH ITS APPL
[3]  
Anosov D. V., 1967, T MAT I STEKLOVA, V90
[4]  
AVILA A., ARXIV14084252V3
[5]   NONUNIFORM HYPERBOLICITY, GLOBAL DOMINATED SPLITTINGS AND GENERIC PROPERTIES OF VOLUME-PRESERVING DIFFEOMORPHISMS [J].
Avila, Artur ;
Bochi, Jairo .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (06) :2883-2907
[6]   On the regularization of conservative maps [J].
Avila, Artur .
ACTA MATHEMATICA, 2010, 205 (01) :5-18
[7]  
Avila A, 2009, ANN SCI ECOLE NORM S, V42, P931
[8]   Removing zero Lyapunov exponents [J].
Baraviera, AT ;
Bonatti, C .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2003, 23 :1655-1670
[9]   The Lyapunov exponents of generic volume-preserving and symplectic maps [J].
Bochi, J ;
Viana, M .
ANNALS OF MATHEMATICS, 2005, 161 (03) :1423-1485
[10]   Perturbation of the Lyapunov spectra of periodic orbits [J].
Bochi, J. ;
Bonatti, C. .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2012, 105 :1-48
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